The paper presents models to characterize the dependence of hardening and strength characteristics of composite materials on damage and strain rate. The results of experimental studies of the behavior of composite materials in a wide range of strain rates are analyzed, and some regularities are determined. On the base of a failure criterion which includes the dependence of failure characteristics on damage and the rate of damage as well, taking into account the dependence of stiffness characteristics on the damage parameters, the stress–strain curves are determined for different strain rates, and they correlate quite well with the results of experimental studies. A method for the experimental determination of the material’s parameters is proposed. Some cases of complex, non-monotonic loading and unloading of composite materials are analyzed.